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Abstract:

A relief print master is created by printing a sequence of layers on top
of each other by an inkjet printing system. The top layer corresponds
with the binary halftoned image that is to be printed by the print master
and the lower intermediate layers are supporting layers. The features in
a lower supporting layer have an area that is larger than the
corresponding features in a higher supporting layer. A circular spread
function is applied on the features of a higher intermediate layer to
increase the area of the features in a lower intermediate layer. By using
a sequence of two non-circular spread functions, the circular spread
function is approximated and the number of required calculations can be
reduced.

Claims:

1-11. (canceled)

12. A method for calculating a series of intermediate bitmaps
corresponding to a series of intermediate layers for creating a relief
print master for printing a digital image, the method comprising the
steps of: calculating a halftone bitmap of the digital image, the
halftone bitmap representing a first intermediate bitmap; and calculating
from the first intermediate bitmap a series of intermediate bitmaps by
applying a spread function on a previous intermediate bitmap to obtain a
next intermediate bitmap; wherein the step of calculating the series of
intermediate bitmaps includes using an alternate sequence of a first
spread function and a second spread function that is different from the
first spread function.

13. The method according to claim 12, wherein the first spread function
includes: generating next to each pixel that corresponds to printing ink
in the series of intermediate bitmaps an additional pixel for printing
ink in four directions corresponding to an XY grid of the previous
intermediate bitmap.

14. The method according to the claim 12, wherein the second spread
function includes: generating next to each pixel that corresponds to
printing ink in the series of intermediate bitmaps an additional pixel
for printing ink in four directions corresponding to an XY grid of the
next intermediate bitmap and in four directions diagonal to the XY grid.

15. The method according to the claim 13, wherein the second spread
function includes: generating next to each pixel that corresponds to
printing ink in the series of intermediate bitmaps an additional pixel
for printing ink in four directions corresponding to an XY grid of then
next intermediate bitmap and in four directions diagonal to the XY grid.

16. A method for creating a relief print master for printing a digital
image using a series of intermediate bitmaps, the method comprising the
steps of: calculating a halftone bitmap of the digital image, the
halftone bitmap representing a first intermediate bitmap; calculating
from the first intermediate bitmap a series of intermediate bitmaps by
applying a spread function on a previous intermediate bitmap to obtain a
next intermediate bitmap; and printing the series of intermediate bitmaps
in an opposite order in which the series of intermediate bitmaps were
calculated to obtain a plurality of intermediate layers; wherein the step
of calculating the series of intermediate bitmaps includes using an
alternate sequence of a first spread function and a second spread
function that is different from the first spread function.

17. The method according to claim 16, wherein the first spread function
includes: generating next to each pixel that corresponds to printing ink
in the series of intermediate bitmaps an additional pixel for printing
ink in four directions corresponding to an XY grid of the previous
intermediate bitmap.

18. The method according to claim 16, wherein the second spread function
includes: generating next to each pixel that corresponds to printing ink
in the series of intermediate bitmaps an additional pixel for printing
ink in four directions corresponding to an XY grid of the next
intermediate bitmap and in four directions diagonal to the XY grid.

19. The method according to claim 17, wherein the second spread function
includes: generating next to each pixel that corresponds to printing ink
in the series of intermediate bitmaps an additional pixel for printing
ink in four directions corresponding to an XY grid of the next
intermediate bitmap and in four directions diagonal to the XY grid.

20. The method according to the claim 16, wherein a previous intermediate
layer is cured before a next intermediate layer is printed.

21. The method according to the claim 17, wherein a previous intermediate
layer is cured before a next intermediate layer is printed.

22. The method according to the claim 18, wherein a previous intermediate
layer is cured before a next intermediate layer is printed.

23. The method according to the claim 19, wherein a previous intermediate
layer is cured before a next intermediate layer is printed.

24. A system for creating a relief print master on a substrate for
printing a digital image by printing a series of intermediate layers from
a series of intermediate bitmaps, the system comprising: a print head
arranged to move in XY directions relative to the substrate to print the
series of intermediate bitmaps; and a computer to calculate the series of
intermediate bitmaps according to claim 12.

25. A system for creating a relief print master on a substrate for
printing a digital image by printing a series of intermediate layers from
a series of intermediate bitmaps, the system comprising: a print head
arranged to move in XY directions relative to the substrate to print the
series of intermediate bitmaps; and a computer to calculate the series of
intermediate bitmaps according to claim 13.

26. A system for creating a relief print master on a substrate for
printing a digital image by printing a series of intermediate layers from
a series of intermediate bitmaps, the system comprising: a print head
arranged to move in XY directions relative to the substrate to print the
series of intermediate bitmaps; and a computer to calculate the series of
intermediate bitmaps according to claim 14.

27. A system for creating a relief print master on a substrate for
printing a digital image by printing a series of intermediate layers from
a series of intermediate bitmaps, the system comprising: a print head
arranged to move in XY directions relative to the substrate to print the
series of intermediate bitmaps; and a computer to calculate the series of
intermediate bitmaps according to claim 15.

28. The system according to claim 24, further comprising a curing source
to cure a previous intermediate layer before a next intermediate layer is
printed.

29. The system according to claim 25, further comprising a curing source
to cure a previous intermediate layer before a next intermediate layer is
printed.

30. The system according to claim 26, further comprising a curing source
to cure a previous intermediate layer before a next intermediate layer is
printed.

31. The system according to claim 27, further comprising a curing source
to cure a previous intermediate layer before a next intermediate layer is
printed.

32. A method for applying a circular spread function on an object in an
image including pixels, the object including a first color that is
different from a second background color, the method comprising a
sequence of the following two steps in either order: generating next to
each pixel that corresponds to the first color in a bitmap an additional
pixel of the same first color in four directions corresponding to an XY
grid of the bitmap and in four directions diagonal to the XY grid to
obtain an intermediate bitmap; and generating next to each pixel that
corresponds to the first color in the intermediate bitmap an additional
pixel of the same first color in the four directions corresponding to the
XY grid of the bitmap.

Description:

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a 371 National Stage Application of
PCT/EP2009/066141, filed Dec. 1, 2009. This application claims the
benefit of U.S. Provisional Application No. 61/139,640, filed Dec. 22,
2008, which is incorporated by reference herein in its entirety. In
addition, this application claims the benefit of European Application No.
08172280.3, filed Dec. 19, 2008, which is also incorporated by reference
herein in its entirety.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to the domain of image processing
methods. It concerns a method for approximating a circular spread
function in a computationally efficient way. It can be used in image
processing for printing three-dimensional objects by means of for example
inkjet printing. The method is particularly suited for the case where the
three-dimensional object is a three-dimensional relief print master. Such
a print master is created by calculating a plurality of intermediate
image layers using the invented method and printing these layers on top
of each other.

[0004] The present invention also relates to a corresponding apparatus.
Such an apparatus may be used for a wide array of applications, for
example for the manufacture of stamps, flexographic, letterpress or
gravure print masters.

[0005] 2. Description of the Related Art

[0006] Three-dimensional printing is a method for creating
three-dimensional objects by depositing or forming thin layers of
material in succession on top of each other so as to build up the desired
three-dimensional structure. It is sometimes called "Rapid Prototyping
and Manufacturing" (RP&M).

[0007] Various methods have been devised to create the thin layers.

[0008] One technique makes use of a bath of polymerisable liquid material.
A thin upper layer of the liquid is cross-linked or hardened in some way,
e.g. via laser light in a pattern which is the same as a cross-section
through the object to be formed. The laser spot is moved across the
surface in accordance with a digital representation of the relevant cross
section. After one layer is completed, the liquid level is raised over a
small distance and the process is repeated. Each polymerised layer should
be sufficiently form-stable to support the next layer.

[0009] In another technique powder is dusted onto a substrate and the
powder is coalesced by some means, e.g. by heating or by the use of a
liquid hardener, in accordance with the shape of the cross-section of the
object to be formed.

[0010] In yet another method, cross linkable or hardenable material is
deposited in the form of drops which are deposited in a pattern according
to the relevant cross-section of the object to be formed.

[0011] Still another method involves dispensing drops of molten material
at an elevated temperature which then solidify on contact with the cooler
work piece.

[0012] There are many items which can be reproduced by three-dimensional
printing. Due to the fact that the materials used to form the object are
subject to many limitations and are generally polymeric in nature, the
final product is not very strong. Therefore three-dimensional printing is
usually reserved for prototyping, for example to create a product design
which can be handled or even tested for certain properties.

[0013] More information on rapid prototyping, three-dimensional printing,
additive fabrication, tooling, and rapid manufacturing is also found in
the Wohlers Report 2008, edited and published by Wohlers Associates,
Inc., OakRidge Business Park 1511 River Oak Drive in Fort Collins, Colo.
80525 USA.

[0014] Printing plates (also referred to as print masters or print forms)
are traditionally manufactured using a combination of image wise exposure
by a laser or light source followed by a chemical or physical developing
step. Such plates are used in a variety of printing methods, such as
flexographic printing, letterpress, offset or gravure printing.

[0015] Flexographic printing or flexography is a printing process where a
flexible print master transfers a fast drying fluid to the printable
substrate. The print master can be a flexible plate mounted on a cylinder
or a cylindrical sleeve. Flexographic printing plates have the features
that define the image that is to be printed in relief, which means that
the ink printing area is raised relative to the non ink printing area.
The result is a relief plate that is capable of transferring ink from an
anilox roll to a substrate. An advantage of flexographic printing is that
almost any material that can run through a web press can be printed on in
this way, including hard surfaced material such as acetate and other
plastic films. Flexography has also been known as "aniline" printing
because of the aniline dye inks that were originally used in the process.

[0016] Letterpress is a printing process where the image is raised as well
and inked to produce an impression.

[0017] Offset printing is a method of printing in which the image is not
printed directly from a plate, but is offset onto a cylinder which
performs the actual printing operation. The printing plate generally has
image-selective hydrophobic regions on a hydrophilic background.

[0018] Gravure printing is a printing process where the image is etched
into a plate or cylinder in the form of recesses or wells. These recesses
or wells are filled with ink and the remaining surface is wiped off, thus
leaving the ink only in the recesses or wells. The image can then be
printed off e.g. onto an absorbent material such as paper.

[0019] There are several additional methods of transferring an image from
a printing plate onto the printing medium. For instance in tampon
printing, a plate comprising an image in relief (or a negative image as
in gravure printing) is inked. Afterwards, ink is transferred to a soft
tampon printing head by contacting the tampon surface with the inked
image. The tampon is then used to print another object, e.g. an object
with an irregular surface.

[0020] Except in offset printing, relief print masters are used which
comprise a substrate with raised parts and recesses. In some of the
printing methods such as in flexography and letterpress, the raised parts
are used for forming the image, while in gravure printing the recesses
form the image. In tampon printing either can be used.

[0021] The smallest individual raised portions on a flexographic printing
plate are particularly vulnerable to damage. One form of damage is Euler
buckling. Euler buckling is the buckling of a thin column into a bow-like
or wave-like shape. Assuming a raised portion of a flexographic printing
plate has a cylindrical shape having a height H and a diameter d, the
critical load which can be applied before buckling is initiated varies
approximately as:

P CR = π 2 * E * I L 2 ( 1 ) ##EQU00001##

wherein E is Young's modulus and I is the moment of inertia. For a
quadratic cross section, the value of I is proportional to the cube of
the thickness, so the danger of mechanical failure increases as a fast
function of the reduction in thickness of a protrusion. Confirmation of
this fact can be found in that it has been known in the flexographic
industry that small dots on flexographic printing plates tend to break
off or wear easily, resulting in discontinuities in tone gradation near
the highlights.

[0022] Gravure rolls are manufactured by an expensive and time consuming
etching process or by means of a diamond stylus which embosses a gravure
roll.

[0023] European patent application with publication number EP 1 428 666 by
Verhoest et al teaches making a flexographic printing plate using an
inkjet apparatus. The plate is formed by applying subsequently on a
substrate at least two image-wise layers of polymerisable ink by an
inkjet printer. Between the application of the first and second layers,
the first layer is immobilized by initiating a polymerization of the ink
using a UV source.

[0024] European patent application with publication number EP 1 437 882 by
Delabastita et al teaches an image processing method for creating a three
dimensional print master. According to the invention a binary digital
image represents the printing surface of a flexographic printing plate. A
topographic operator, such as a circular symmetric smoothing filter, is
applied on this binary halftone image resulting in a contone image of
which the densities represent the heights of a relief print master. The
contone image is then conceptually sliced to obtain intermediate binary
layers which, when printed on top of each other, form a three-dimensional
print master. The effect of the smoothing filter is that around each
pixel in an upper intermediate layer a circle of identical pixels is
replicated in a lower intermediate layer. As a result, every lower
intermediate layer always entirely supports any upper intermediate layer.

[0025] One problem with the latter technique is that it requires many
computations. It is therefore desirable to come up with a method to
calculate the intermediate layers in a way that requires fewer
calculations.

SUMMARY OF THE INVENTION

[0026] A method according to a preferred embodiment of the current
invention takes advantage of the observation that exact shape of the
intermediate layers for creating a three-dimensional print master is not
very important as long as the condition is fulfilled that every lower
intermediate layer supports the higher intermediate layers.

[0027] This observation enables to use a calculation method that only
approximates a circular spread function (as results from using a circular
symmetric smoothing filter in the Delabastita method).

[0028] A method according to a preferred embodiment of the current
invention starts from the binary halftone bitmap in which pixels that are
to print ink have a first color and pixels that are not to print ink have
a second color. The method applies in a first step a first spread
function on the pixels having the first color to obtain a first
intermediate bitmap.

[0029] Such a first spread function consists for example of adding to a
pixel having the first color additional pixels having a same color to the
left, right, bottom and top of the original pixel. A first intermediary
bitmap is obtained by applying this first spread function to all the
pixels of the bitmap having the first color and making the union of the
results.

[0030] Such an operation, which essentially consists of four times
replicating pixels having the first color in the horizontal and vertical
directions can be computationally efficiently implemented, for example
using a GPU ("Graphics Processing Unit").

[0031] In a second step a second spread function, different from the first
spread function is applied on the first intermediate bitmap to obtain a
second intermediate bitmap.

[0032] A second spread function consists for example of adding to a pixel
having the first color an additional pixel having the same color to the
left, right, bottom, top and along the four diagonal directions of the
original pixel. By applying this second spread function to all the pixels
having the first color and making the union of the result, a second
intermediary bitmap is obtained.

[0033] Just like the first spread function, the second spread function can
be efficiently implemented using a GPU.

[0034] This process of applying alternately a first and a second spread
function on a previous intermediate bitmap is repeated as often as
necessary. Every subsequent intermediate bitmap is slightly larger than a
previous intermediate bitmap and is hence capable of supporting it.

[0035] It was surprisingly found that by proper selection of a first and
second spread function, the circular spread function that results from
the Delabastita method is sufficiently approximated for printing a
three-dimensional print master such as a flexographic print master.

[0036] Besides a method for calculating intermediate bitmaps, the current
invention also includes a data processing system for calculating the
intermediate bitmaps and a method and an apparatus for printing the
intermediate bitmaps to form a print master.

[0037] The above and other elements, features, steps, characteristics and
advantages of the present invention will become more apparent from the
following detailed description of the preferred embodiments with
reference to the attached drawings.

[0039] FIG. 2 shows a cross section of a relief print master created by
using a preferred embodiment of the current invention.

[0040] FIG. 3 shows a perspective view of a relief print master created by
using a preferred method according to the current invention for printing
a halftoned image object, a text object and a graphic object.

[0042]FIG. 5 shows a second spread function different from the first
spread function.

[0043]FIG. 6 shows a spread of a cluster of pixels using the first spread
function.

[0044]FIG. 7 shows that the spread function in FIG. 4 can be obtained by
applying a logical OR operation on a bitmap obtained with a vertical
spread function and a bitmap obtained with a horizontal spread function.

[0045]FIG. 8 shows that the spread function in FIG. 5 can be obtained by
a sequence of a vertical spread function followed by a horizontal spread
function.

[0046]FIG. 9 shows a first preferred embodiment of an apparatus for
creating a relief print master according to the current invention.

[0047]FIG. 10 shows a second preferred embodiment of an apparatus for
creating a relief print master according to the current invention.

[0048]FIG. 11 shows a variation of the second preferred embodiment in
which a printing plate is replaced by a printing sleeve.

[0049] FIG. 12A to FIG. 12J show a sequence of intermediate bitmaps for
forming intermediate layers to create a relief print master according to
the current invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0050] The drawings in the figures are for explanatory purposes only. The
different parts in the drawings are not necessarily using consistent
scales.

Rendering of a Digital Image

[0051] The image that is to be printed can be any digital image that can
be represented as a raster bitmap.

[0052] A typical image comprises multiple objects such as photographs,
graphic objects such as polygons and line work and text objects.

[0053] These objects are usually generated using a page description
language and are rendered into a digital image by a raster image
processor (RIP) such as made available by the company Adobe Systems
Incorporated.

[0054] The image can be monochrome or color. In the latter case, the color
image is first separated into a set of ink separations that correspond
with a set of corresponding printing inks.

[0055] Halftoning refers to an image processing technique for rendering
images having multiple densities on a rendering system with a restricted
density resolution. For example, a digital image has pixels with a
density resolution of 8 bits (256 shades) and is rendered on a binary
printing system having only two shades of density corresponding with ink
or no ink.

[0056] A binary halftoned image is represented by a halftone bitmap in
which the color of every bit indicates whether ink or no ink is to
printed at the corresponding location.

[0058] In AM halftoning, the grid points of a periodical grid contain
clusters of pixels ("halftone dots") of which the sizes are modulated to
simulate different densities in the digital image. An example of a moire
free AM halftoning method for color images is disclosed in the U.S. Pat.
No. 5,155,599 invented by Delabastita and assigned to Agfa-Graphic NV.
FIG. 1 shows an example of a degrade that has been rendered with AM
screening.

[0059] In FM screening, the distance between fixed sized halftone dots is
varied to simulate different densities. An example of an FM screening
method particularly suitable for creating print masters with ink jet is
disclosed in U.S. Pat. No. 6,962,400 invented by Minnebo et al. and
assigned to Agfa-Graphics NV.

[0060] Hybrid screening is a mixed form of AM and FM halftoning in which a
combination is used of different halftone dot sizes and distances to
modulate densities in the original digital image. An example of hybrid
screening is the "Sublima XM screening" product manufactured and marketed
by Agfa-Graphics NV.

[0061] Whereas a preferred embodiment of the current invention uses AM or
XM screening, it can just as well be used in combination with FM
screening.

[0063] In a preferred embodiment of the current invention, the print
master is a positive print master such as a letterpress or a flexographic
print master.

[0064] Optionally it can be a negative print master, in which case the ink
is contained in wells with reference to its top surface. An example is a
gravure print master or a negative tampon print master.

[0065] FIG. 2 shows a cross section of a print master created with a
system according to a preferred embodiment of the current invention.

[0067] Two forms of flexographic printing supports 200 can be
distinguished: a sheet form and a cylindrical form (sleeve). If the print
master is created as a sheet form on a flatbed inkjet device (such as the
one shown in FIG. 9), the mounting of the sheet form on a sleeve
introduces mechanical distortions that show up as anamorphic distortion
in the printed image. This distortion is preferably compensated by an
anamorphic pre-compensation in an image processing step prior to
halftoning.

[0068] Creating the print master on a sleeve, either on a sheet form
mounted on the sleeve or directly on a sleeve, for example a seamless
sleeve, avoids the problem of geometric distortion altogether. Therefore
sleeve forms provide improved registration accuracy and faster change
over time on press. Furthermore, sleeves may be well-suited for mounting
on an inkjet printer having a rotatable drum. In FIG. 2, a support 200
provides the necessary strength and dimensional stability for handling
and mounting the print master. Seamless sleeves have applications in the
flexographic printing of continuous designs such as in wallpaper,
decoration, gift wrapping paper and packaging.

[0069] The term "flexographic printing support", as used in the preferred
embodiments of the present invention, encompasses two types of support:

[0070] 1) a support without elastomeric layers on its surface; and

[0071] 2) a support with one or more elastomeric layers on its surface.

[0072] In a preferred embodiment, the flexographic printing support is a
sleeve, which encompasses a basic sleeve and a flexographic printing
sleeve.

[0073] The term "basic sleeve" means a sleeve without elastomeric layers
on its outer surface, while the term "flexographic printing sleeve" means
a basic sleeve having one or more elastomeric layers on its outer
surface.

[0074] Although here below the type of materials, the wall thicknesses, .
. . are written for sleeves, the same type of materials, wall
thicknesses, . . . can be used for flexographic printing supports having
a sheet form.

Basic Sleeves

[0075] The basic sleeve can be any material that is conventionally used to
prepare flexographic printing masters. For good printing results, a
dimensionally stable support is required. Basic sleeves, often also
called a sleeve base, ordinarily consist of composites, such as epoxy or
polyester resins reinforced with glass fibre or carbon fibre mesh.
Metals, such as steel, aluminium, copper and nickel, and hard
polyurethane surfaces (e.g. durometer 75 Shore D) can also be used.

[0076] The sleeve may be formed from a single layer or multiple layers of
flexible material, as for example disclosed by US 2002/0046668 (ROSSINI).
Flexible sleeves made of polymeric films can be transparent to
ultraviolet radiation and thereby accommodate backflash exposure for
building a floor in the cylindrical printing element. Multiple layered
sleeves may include an adhesive layer or tape between the layers of
flexible material. Preferred is a multiple layered sleeve as disclosed in
U.S. Pat. No. 5,301,610 (DU PONT). The sleeve may also be made of
non-transparent, actinic radiation blocking materials, such as nickel or
glass epoxy.

[0077] Depending upon the type of tubing and the number of layers of mesh
applied, the wall thickness of these sleeve bases varies. The sleeve
typically has a wall thickness from 0.1 to 1.5 mm for thin sleeves and
from 2 mm to as high as 100 mm for other sleeves.

[0078] For thick sleeves often combinations of a hard polyurethane surface
with a low-density polyurethane foam as an intermediate layer combined
with a fiberglass reinforced composite core are used as well as sleeves
with a highly compressible surface present on a sleeve base.

[0079] Depending upon the specific application, sleeve bases may be
conical or cylindrical. Cylindrical sleeve bases are used primarily in
flexographic printing.

[0080] As press speeds have increased, press bounce has become a more
frequent problem. Various approaches can be taken to reduce press bounce,
including the use of cushioned sleeves. Sleeves come in different
constructions, e.g. with a hard or a compressible core or surface, with
varying wall thicknesses.

[0081] The basic sleeve or flexographic printing sleeve is stabilized by
fitting it over a steel roll core known as an air mandrel or air
cylinder. Air mandrels are hollow steel cores which can be pressurized
with compressed air through a threaded inlet in the end plate wall. Small
holes drilled in the cylindrical wall serve as air outlets. The
introduction of air under high pressure permits it to float into position
over an air cushion. Certain thin sleeves are also expanded slightly by
the compressed air application, thereby facilitating the gliding movement
of the sleeve over the roll core.

[0082] Foamed adapter or bridge sleeves are used to "bridge" the
difference in diameter between the air-cylinder and a flexographic
printing sleeve containing the printing relief. The diameter of a sleeve
depends upon the required repeat length of the printing job.

Flexographic Printing Sleeves

[0083] A flexographic printing sleeve is a basic sleeve provided with one
or more elastomeric layers. The elastomeric layers may be any material
that is conventionally used to prepare flexographic printing masters. The
elastomeric layers are preferably partially or fully cured photopolymer
layers, but can also be rubber or polyurethane layers. It is also
possible to use a partially or fully cured conventional UV exposure
flexographic printing form precursor as flexographic printing sleeve. A
wide variety of such conventional flexographic printing form precursors
are commercially available.

[0084] A printing relief can be formed in several ways on the flexographic
printing sleeve. In a preferred embodiment the relief is formed by inkjet
printing on the one or more elastomeric layers already present as an
"elastomeric floor 220". In the latter, the one or more elastomeric
layers are preferably partially cured layers to enhance the adhesion of
the relief jetted onto the elastomeric layers. Alternatively the
elastomeric floor may also be applied to the surface of the basic sleeve
by inkjet printing.

[0085] In another preferred embodiment, the elastomeric layers are fully
cured and the relief is formed by laser engraving. In laser engraving,
the elastomeric layers of a different hardness can be used to obtain the
desired hardness.

[0086] In another preferred embodiment the flexographic printing sleeve is
prepared by a coating method as disclosed in WO 2008/034810 (AGFA
GRAPHICS).

[0087] Different types of printing applications require flexographic
printing forms with differing degrees of hardness. Softer flexographic
printing forms are more suited for rough substrates because they can
better cover the highs and lows. The harder flexographic printing forms
are used for even and smooth substrates. The optimum hardness of a
flexographic printing form also depends on whether the image is solid or
halftone. Softer flexographic printing forms will transfer the ink better
in solid areas, though harder flexographic printing forms have less dot
gain. The hardness is a measure of the printing form's mechanical
properties which is measured in degree of Shore A. For example, printing
on corrugated board requires usually a hardness of 35° Shore A,
whereas for reel presses 65° to 75° Shore A is a standard.

[0088] Depending on the substrate to be printed upon, the hardness and
thickness of the flexographic printing form have to be adjusted by
controlling the amount of the curable liquid that is printed, its
composition and its degree of curing. Depending on the application, the
relief depth varies from 0.2 to 4 mm, preferably from 0.4 to 2 mm.

[0089] In a preferred embodiment of the current invention, a relief is
applied by an inkjet printing device by applying image-wise on a support
subsequent layers of radiation curable liquid by an inkjet printing
device whereby an applied layer is preferably immobilized using a curing
device before a subsequent layer is applied. The curing does not have to
be a full cure, but can be a partial cure. Optionally some of the layers
are not cured directly after jetting the layer, but after jetting of a
subsequent layer. In a preferred embodiment, each applied layer is
immobilized using the curing device before a subsequent layer is applied.

[0090] In a preferred embodiment of the present invention of the method
for making a flexographic printing master, the relief includes a
so-called "mesa relief" as shown by the flexographic printing master
(250) in FIG. 2. The layers (212) together define a "mesa relief". Such a
mesa relief is only present in those parts of the flexographic printing
master comprising image features such as text, graphics and halftone
images. In extended areas where such image features are absent, there is
no mesa relief.

[0091] A mesa relief preferably has a height (242) in a range from 50
μm to 1 mm, for example 0.5 mm.

[0092] The layers (210), (211) and (212) in FIG. 2 define the actual
printing relief of the flexographic printing master. The layers (210) and
(211) in FIG. 2 define the image relief. The top layer (230) corresponds
with a halftone bitmap that defines the image that is to be printed by
the printing master. The layers (210) are preferably identical in shape
and size as the top layer (230), producing a vertical relief slope and
defining a "top hat segment". Such a top hat may have a height (240)
between 10 and 500 μm and preferably between 20 and 200 μm. A
vertical relief slope for a top hat segment has the advantage that the
printing surface (230) remains consistent during printing, even when
pressure variations occur between the print master and the anilox roller
or between the print master and the printable substrate, or when the
printing master wears off.

[0093] The intermediate layers (211), together forming a sloped segment,
are preferably printed with a slope having an angle (235) that is less
than 90 degrees. The angle can be between 25 and 75 degrees, preferably
between 40 and 60 degrees, for example 50 degrees. The angle (235) can be
controlled by controlling the height (241) of the individual layers,
their number and the difference in size between subsequent layers.

[0094] Using a lower slope angle (235) has the advantage that small
features on the print master will suffer less from buckling. The total
height (241) of the intermediate layers (211) is for example between 30
μm and 700 μm, preferably between 50 μm and 250 μm.

[0095] In a more preferred embodiment of the current invention, the
intermediate layers (210), (211) and (212) are printed in multiple passes
with an ink jet printer that jets a radiation curable liquid in
combination with a curing device. Each intermediate layer is solidified
by a curing device immediately after printing. Especially the upper layer
(232) of the mesa relief is preferably only partially cured for ensuring
a good adhesion with the lowest intermediate layer (231) of the sloped
segment (211). Optionally a final curing step is carried out to further
harden the layers after all of them have been printed.

[0096] The mesa relief is preferably printed on an elastomeric support
floor (220) that provides the necessary resilience to the flexographic
printing master. Such an elastomeric floor can, for example, be obtained
by layer-wise spraying or jetting a radiation curable liquid on the
support and curing the layers with a UV curing source. The height (243)
of an elastomeric floor (220) is preferably between 0.3 mm and 2 mm.

[0097] The elastomeric floor (220) may itself be supported by a support
(200). A support (200) of a sheet form typically has a height (244) from
0.005 to 0.127 cm. A preferred height (244) for the sheet form is 0.007
to 0.040 cm. A sleeve form typically has a wall height (244) from 0.1 to
1 mm for thin sleeves and from 1 to as much as 100 mm for other sleeves.
The selection of the height (244) depends upon the application.

First and Second Spread Function

[0098] In this part of the text the concepts of a first and a second
spread function are elaborated which are of importance in the remainder
of the text.

[0099] In a preferred embodiment of the current invention, a spread of a
binary pixel having a first color on a background having a second color
refers to replicating that pixel so that a contiguous cluster of pixels
having the same first color surrounds the original pixel. If the spread
of a first and a second pixel overlap, the union is taken of both
spreads. A spread function defines the spread of a single isolated pixel.

[0100]FIG. 4 shows an example of a first spread function. The "black"
pixel is the one having the "first" color and on which the spread is
applied. The "grey" pixels are the ones that have been added by the
spread and also correspond with the first color (in FIG. 4 they are only
rendered in grey to enable to distinguish between the original and added
pixels). In the example in FIG. 4, a pixel is replicated to the left, to
the right, to the bottom and to the top of the original pixel, i.e. to
the four XY directions of the bitmap.

[0101]FIG. 5 shows an example of a second spread function. In this
example a pixel is replicated to the left, to the right, to the bottom
and to the top of the original pixel, i.e. to the four XY directions of
the bitmap as well to the four diagonal directions.

[0102] In FIG. 6 the second spread function is applied on a set of three
neighboring pixels having the same first color. Applying the spread on
each pixel results in three overlapping pixel clusters of the same first
color of which the union is taken. Arithmetically speaking, the effect of
the spread of a first pixel is combined with a bitwise logical OR
function with the effect of the spread of the other pixels in a bitmap.

[0103]FIG. 7 demonstrates a concept for an efficient implementation of
the first spread function. The effect of the spread function in FIG. 4 is
obtained by applying separately a horizontal spread (HS) and a vertical
spread (VS) on the original pixel and using a logical OR function to
combine the two results. A horizontal spread of a pixel is efficiently
performed by applying a logical OR function to a pixel with its
translation to the left and its translation to the right. Such a
translation is preferably implemented using unsigned integer arithmetic.
In a similar way a vertical spread is efficiently performed. These
operations are preferably implemented simultaneously on a group of bits
in a bitmap, for example, all the bits in a 16 bit or 32 bit word.

[0104] For example, a first eight bit word BM containing eight binary
pixels (whereby the most significant bit in the word corresponds with the
left most pixel and the least significant bit with the right most pixel)
is transformed into a second word BM' by applying a horizontal spread
function using the following computer instructions (in meta C computer
language and assuming unsigned eight bit arithmetic):

[0105] BM'=BM(BM<<1)(BM>>1)(0bL0000000)(0b0000000R)

[0106] wherein:

[0107] refers to a bitwise logical OR operation on a word

[0108] >>1 refers to a shift to right shift operation of the entire
word; [0109] <<1 refers to a shift to left shift operation of the
entire word;

[0110] L refers to the value of the carry over bit resulting from the
right shift operation of the left neighbor word;

[0111] R refers to the value of the carry over bit resulting from the left
shift operation of the right neighbor word.

[0112] As FIG. 8 demonstrates, the second spread function can be very
efficiently implemented by applying on a pixel having the first color
first a vertical spread (VS), and by subsequently applying on this
vertical spread a horizontal spread (HS) or vice versa.

[0113] Similarly, a vertical spread function VS is implemented using the
following computer instructions:

[0114] BM'=BMBMUBML

[0115] wherein BMU and BML refer to the words having one position higher
and lower than BM in the bitmap.

Calculating the Intermediate Layers 210, 211 and 212

[0116] The top layer 230 and intermediate layers 210 correspond with the
halftone bitmap. This binary halftoned bitmap is directly obtainable from
the raster image processor.

[0117] The intermediate layers 211 are obtained by repetitively applying a
spread function to the binary halftoned bitmap.

[0118] According to a preferred embodiment of the current invention, such
a spread function is approximated by subsequently applying a first and a
second spread function starting from the digital halftone bitmap

[0119] This is demonstrated by means of the FIG. 12A to FIG. 12J where the
operation is shown for a single bit in the halftone bitmap. It was
mentioned before that the same operation should be performed on all the
bits of the halftone bitmap and that the results of these operations
should be combined by means of a bitwise logical OR operation.

[0120] According to a first step of a preferred method, a first spread
function is applied to a single pixel in FIG. 12A to obtain a first
intermediate bitmap comprising a first cluster of pixels in FIG. 12B.

[0121] In a second step a second spread function is applied on the first
intermediate bitmap in FIG. 12B. This results in a second intermediate
bitmap in FIG. 12C.

[0122] By repeating the first and second step, a sequence of intermediate
bitmaps shown in FIG. 12D to FIG. 12J is obtained.

[0123] As the sequence of FIG. 12A to 12J indicates, the clusters in the
intermediate bitmaps closely approximate circles. The effect of
alternating a first and a second--different--spread function apparently
approximates a circular spread function.

[0124] Comparing FIG. 12F with FIG. 12H leads to the following
observations. The increase 1210 of the radius measured along a horizontal
tangent line by applying a first and a second spread function is 2
pixels. The increase 1220 of the radius measured along a 45 degree
tangent line by applying a first and a second spread function is ( 3/2)*
{square root over (2)}=2.12 pixels. The growth along the 45 degree
tangent lines is only 1.06 times larger than the growth along the
horizontal and vertical tangent lines and this provides part of the
explanation why the sequence of the first and second spread function
approximates a circular spread function.

[0125] When the sequence of the first and second spread functions is
repeated many times, the shape of the combined spread function starts to
approximate an octagon and ultimately a square. This however is without
effect for creating a print master since the exact shape of the
intermediate layers 211 is not relevant as long as a lower intermediate
layer completely supports a higher intermediate layer.

[0126] The first spread functions shown in FIG. 4 and the second spread
function shown in FIG. 5 are preferred embodiments for the current
invention. However, a sequence of different spread functions can be used
for achieving the same objective. In general any sequence of spread
functions can be used that enable efficient computing of intermediate
bitmaps and fulfill the requirement that a next intermediate bitmap
completely supports a previous intermediate layer.

[0127] The intermediate layers that define the mesa relief can be
calculated using a variation of the above described technique. In that
case the starting point is the lowest intermediate layer 231 of the
relief part 211. On this lowest layer 231 a substantial spread, for
example of 0.5 mm is applied using the above described techniques, i.e.
by applying multiple times a spread function that is approximated by a
sequence of a first and a second spread function. This results in an
upper layer 232 of the mesa relief. On this upper layer 232 again a
spread function is applied to subsequently calculate the lower
intermediate layers 212 of the mesa relief.

Creating the Print Master

[0128] A print master 250 is created by printing the intermediate bitmaps
in the reverse order that they were calculated. This means that first the
layers defining the mesa relief are printed from lowest to highest,
subsequently the intermediate layers 211 from lowest to highest and
finally the layers defining the top hat relief from lowest to highest.
The last layer that is to be printed is the top layer 230. For this
purpose an apparatus shown in FIG. 9, FIG. 10 or in FIG. 11 can be used.

[0129] In FIG. 9 a carriage 900 is mounted so that it can move in a Y
direction with regard to a printed substrate 920. On the carriage a print
head 910 is mounted that can move in an X direction with regard to a
printable substrate 920. Additionally the print head can move in a Z
direction perpendicular to the substrate 920.

[0130] The print head is coupled to a curing source 930 for curing the
printed ink during printing and optionally a laser profilometer 940 for
measuring the profile of the printed layers.

[0131] The print head scans the printable substrate 920 along the XY
dimensions and prints an intermediate bitmap that results in an
intermediate layer calculated using a method according to a preferred
embodiment of the current invention. During the scan the curing source
930 solidifies the printed ink. The profile meter 940 measures the
profile of the printed layers and controls the Z position of the print
head.

[0132] An alternative preferred embodiment is shown in FIG. 10. A sleeve
1025 is mounted on a drum 1000 that is driven by a motor 1060 in a
rotational direction X, which corresponds with a fast scan dimension. The
sleeve carries a sheet of support layer 1020.

[0133] A printhead 1030 is mounted on a carriage (not shown) that can move
in the Y direction parallel to the axle of the drum and which corresponds
with a slow scan dimension.

[0134] During operation, the combination of the rotation X and translation
Y of the printhead enables to print an intermediate bitmap on the
substrate. During the printing, partial curing takes place of a printed
intermediate layer by the curing source 1010. 1040 is a profile meter to
control the distance between the print head and the substrate in a Z
direction.

[0135] Optionally the printed intermediate layers can be subject to a post
curing step by rotating the drum 1000 while a final curing source 1050 is
turned on.

[0136] A variation of the preferred embodiment in FIG. 10 is shown in FIG.
11, except that the support layer 1120 in this case is seamless, which is
a preferred embodiment according to the current invention. This set up
enables the printing on sleeves in a continuous and seamless fashion,
which is a preferred embodiment according to the current invention.
According to this preferred embodiment, the position of the printhead
1030 moves linearly in the slow scan dimension Y as a function of the
angular rotation of the drum in the X direction. The effect of this is
that every nozzle of the printhead describes a continuous and spiral
motion relative to a fixed position on the drum

Curable Liquid Composition (Ink)

[0137] The ink that is used for printing the intermediate layers 210, 211
and 212 is a liquid that is curable by actinic radiation which can be UV
light, IR light or visible light. Preferably the radiation curable liquid
is a UV curable liquid.

[0138] The radiation curable liquid preferably contains at least a
photo-initiator and a polymerisable compound. The polymerisable compound
can be a monofunctional or polyfunctional monomer, oligomer or
pre-polymer or a combination thereof.

[0139] The radiation curable liquid may be a cationically curable liquid
but is preferably a free radical curable liquid.

[0140] The free radical curable liquid preferably contains substantially
acrylates rather than methacrylates for obtaining a high flexibility of
the applied layer. Also the functionality of the polymerisable compound
plays an important role in the flexibility of the applied layer.
Preferably a substantial amount of monofunctional monomers and oligomers
are used.

[0141] In a preferred embodiment of the present invention, the radiation
curable liquid includes:

[0144] In a more preferred embodiment of the present invention, the
radiation curable liquid includes an aliphatic urethane acrylate.
Aromatic type urethane acrylates are less preferred.

[0145] In an even more preferred embodiment, the urethane acrylate is a
urethane monoacrylate. Commercial examples include GENOMER® 1122 and
EBECRYL® 1039.

[0146] The flexibility of a given urethane acrylate can be enhanced by
increasing the linear molecular weight between cross links. Polyether
type urethane acrylates are for flexibility also more preferred than
polyester type urethane acrylates.

[0147] Preferably the radiation curable liquid does not include amine
modified polyether acrylates which reduce the flexibility of the cured
layer.

[0148] An elastomer or a plasticizer is preferably present in the
radiation curable liquid for improving desired flexographic properties
such as flexibility and elongation at break.

[0149] The radiation curable liquid may contain a polymerization inhibitor
to restrain polymerization by heat or actinic radiation.

[0150] The radiation curable liquid may contain at least one surfactant
for controlling the spreading of the liquid.

[0151] The radiation curable liquid may further contain at least one
colorant for increasing contrast of the image on the flexographic print
master.

[0152] The radiation curable liquid may further contain at least one acid
functionalized monomer or oligomer.

[0153] The radiation curable liquid preferably has a viscosity at a shear
rate of 100 s-1 and at a temperature between 15 and 70° C. of not
more than 100 mPas, preferably less than 50 mPas, and more preferably
less than 15 mPas.

*Monofunctional Monomers*

[0154] Any polymerisable monofunctional monomer commonly known in the art
may be employed. Particular preferred polymerisable monofunctional
monomers are disclosed in paragraphs [0054] to [0058] of EP 1637926 A
(AGFA).

[0155] Two or more monofunctional monomers can be used in combination.

[0156] The monofunctional monomer preferably has a viscosity smaller than
30 mPas at a shear rate of 100 s-1 and at a temperature between 15 and
70° C.

*Polyfunctional Monomers and Oligomers*

[0157] Any polymerisable polyfunctional monomer and oligomer commonly
known in the art may be employed. Particular preferred polyfunctional
monomers and oligomers are disclosed in paragraphs [0059] to [0063] of EP
1637926 A (AGFA).

[0158] Two or more polyfunctional monomers and/or oligomers can be used in
combination.

[0159] The polyfunctional monomer or oligomer preferably has a viscosity
larger than 50 mPas at a shear rate of 100 s-1 and at a temperature
between 15 and 70° C.

*Acid Functionalized Monomers and Oligomers*

[0160] Any polymerisable acid functionalized monomer and oligomer commonly
known in the art may be employed. Particular preferred acid
functionalized monomers and oligomers are disclosed in paragraphs [0066]
to [0070] of EP 1637926 A (AGFA).

*Photo-Initiators*

[0161] The photo-initiator, upon absorption of actinic radiation,
preferably UV-radiation, forms free radicals or cations, i.e. high-energy
species inducing polymerization and crosslinking of the monomers and
oligomers in the radiation curable liquid.

[0162] A preferred amount of photo-initiator is 1 to 10% by weight, more
preferably 1 to 7% by weight, of the total radiation curable liquid
weight.

[0163] A combination of two or more photo-initiators may be used. A
photo-initiator system, comprising a photo-initiator and a co-initiator,
may also be used. A suitable photo-initiator system comprises a
photo-initiator, which upon absorption of actinic radiation forms free
radicals by hydrogen abstraction or electron extraction from a second
compound, the co-initiator. The co-initiator becomes the actual
initiating free radical.

[0164] Irradiation with actinic radiation may be realized in two steps,
each step using actinic radiation having a different wavelength and/or
intensity. In such cases it is preferred to use 2 types of
photo-initiators, chosen in function of the different actinic radiation
used.

[0165] Suitable photo-initiators are disclosed in paragraphs [0077] to
[0079] of EP 1637926 A (AGFA).

*Inhibitors*

[0166] Suitable polymerization inhibitors include phenol type
antioxidants, hindered amine light stabilizers, phosphor type
antioxidants, hydroquinone monomethyl ether commonly used in
(meth)acrylate monomers, and hydroquinone, methylhydroquinone,
t-butylcatechol, pyrogallol may also be used. Of these, a phenol compound
having a double bond in molecules derived from acrylic acid is
particularly preferred due to its having a polymerization-restraining
effect even when heated in a closed, oxygen-free environment. Suitable
inhibitors are, for example, SUMILIZER® GA-80, SUMILIZER® GM and
SUMILIZER® GS produced by Sumitomo Chemical Co., Ltd.

[0167] Since excessive addition of these polymerization inhibitors will
lower the sensitivity to curing of the radiation curable liquid, it is
preferred that the amount capable of preventing polymerization be
determined prior to blending. The amount of a polymerization inhibitor is
generally between 200 and 20,000 ppm of the total radiation curable
liquid weight.

*Oxygen Inhibition*

[0168] Suitable combinations of compounds which decrease oxygen
polymerization inhibition with radical polymerization inhibitors are:
2-benzyl-2-dimethylamino-1-(4-morpholinophenyl)-butane-1 and
1-hydroxy-cyclohexyl-phenyl-ketone; 1-hydroxy-cyclohexyl-phenyl-ketone
and benzophenone; 2-methyl-1
[4-(methylthio)phenyl]-2-morpholino-propane-1-on and diethylthioxanthone
or isopropylthioxanthone; and benzophenone and acrylate derivatives
having a tertiary amino group, and addition of tertiary amines. An amine
compound is commonly employed to decrease an oxygen polymerization
inhibition or to increase sensitivity. However, when an amine compound is
used in combination with a high acid value compound, the storage
stability at high temperature tends to be decreased. Therefore,
specifically, the use of an amine compound with a high acid value
compound in ink-jet printing should be avoided.

[0169] Synergist additives may be used to improve the curing quality and
to diminish the influence of the oxygen inhibition. Such additives
include, but are not limited to ACTILANE® 800 and ACTILANE® 725
available from AKZO NOBEL, EBECRYL® P115 and EBECRYL® 350 available
from UCB CHEMICALS and CD 1012, CRAYNOR® CN 386 (amine modified
acrylate) and CRAYNOR® CN 501 (amine modified ethoxylated
trimethylolpropane triacrylate) available from CRAY VALLEY.

[0170] The content of the synergist additive is in the range of 0 to 50%
by weight, preferably in the range of 5 to 35% by weight, based on the
total weight of the radiation curable liquid.

*Plasticizers*

[0171] Plasticizers are usually used to improve the plasticity or to
reduce the hardness of adhesives, sealing compounds and coating
compositions. Plasticizers are liquid or solid, generally inert organic
substances of low vapor pressure.

[0172] Suitable Plasticizers are Disclosed in Paragraphs [0086] to [0089]
of EP 1637926 A (AGFA).

[0173] The amount of plasticizer is preferably at least 5% by weight, more
preferably at least 10% by weight, each based on the total weight of the
radiation curable liquid.

[0174] The plasticizers may have molecular weights up to 30 000 but are
preferably liquids having molecular weights of less than 5,000.

*Elastomers*

[0175] The elastomer may be a single binder or a mixture of various
binders. The elastomeric binder is an elastomeric copolymer of a
conjugated diene-type monomer and a polyene monomer having at least two
non-conjugated double bonds, or an elastomeric copolymer of a conjugated
diene-type monomer, a polyene monomer having at least two non-conjugated
double bonds and a vinyl monomer copolymerizable with these monomers.

[0176] Preferred elastomers are disclosed in paragraphs [0092] and [0093]
of EP 1637926 A (AGFA).

*Surfactants*

[0177] The surfactant(s) may be anionic, cationic, non-ionic, or
zwitter-ionic and are usually added in a total quantity below 20% by
weight, more preferably in a total quantity below 10% by weight, each
based on the total radiation curable liquid weight.

[0178] A fluorinated or silicone compound may be used as a surfactant,
however, a potential drawback is bleed-out after image formation because
the surfactant does not cross-link. It is therefore preferred to use a
copolymerizable monomer having surface-active effects, for example,
silicone-modified acrylates, silicone modified methacrylates, fluorinated
acrylates, and fluorinated methacrylates.

*Colorants*

[0179] Colorants may be dyes or pigments or a combination thereof. Organic
and/or inorganic pigments may be used.

[0181] Suitable pigments are disclosed in paragraphs [0098] to [0100] of
EP 1637926 A (AGFA).

[0182] The pigment is present in the range of 0.01 to 10% by weight,
preferably in the range of 0.1 to 5% by weight, each based on the total
weight of radiation curable liquid.

*Solvents*

[0183] The radiation curable liquid preferably does not contain an
evaporable component, but sometimes, it can be advantageous to
incorporate an extremely small amount of a solvent to improve adhesion to
the ink-receiver surface after UV curing. In this case, the added solvent
may be any amount in the range of 0.1 to 10.0% by weight, preferably in
the range of 0.1 to 5.0% by weight, each based on the total weight of
radiation curable liquid.

*Humectants*

[0184] When a solvent is used in the radiation curable liquid, a humectant
may be added to prevent the clogging of the nozzle, due to its ability to
slow down the evaporation rate of radiation curable liquid.

[0185] Suitable humectants are disclosed in paragraph [0105] of EP 1637926
A (AGFA).

[0186] A humectant is preferably added to the radiation curable liquid
formulation in an amount of 0.01 to 20% by weight of the formulation,
more preferably in an amount of 0.1 to 10% by weight of the formulation.

*Biocides*

[0187] Suitable biocides include sodium dehydroacetate, 2-phenoxyethanol,
sodium benzoate, sodium pyridinethion-1-oxide, ethyl p-hydroxy-benzoate
and 1,2-benzisothiazolin-3-one and salts thereof. A preferred biocide for
the radiation curable liquid suitable for the method for manufacturing a
flexographic print master according to the present invention, is
PROXEL® GXL available from ZENECA COLOURS.

[0188] A biocide is preferably added in an amount of 0.001 to 3% by
weight, more preferably in an amount of 0.01 to 1.00% by weight, each
based on radiation curable liquid.

*Preparation of Radiation Curable Liquids*

[0189] The radiation curable liquid may be prepared as known in the art by
mixing or dispersing the ingredients together, optionally followed by
milling, as described for example in paragraphs [0108] and [0109] of EP
1637926 A (AGFA).

Print Head

[0190] An example of a print head according to the current invention is
capable to eject droplets having a volume between 0.1 and 100 pl. and
preferably between 1 and 30 pl. Even more preferably the droplet volume
is in a range between 1 pl and 8 pl. Even more preferably the droplet
volume is only 2 or 3 pl.

[0191] The dot placement precision with regard to the theoretical
addressable print grid is for example less than +/-3 micron in 99.73%
(three sigma) of the printed pixels.

[0192] The print head has an addressable grid having a square pitch of for
example 70 micrometer.

Curing Source

[0193] Just after the deposition of ink drops by the print head on the
substrate they are exposed by a curing source. This provides
immobilization and prevents the droplets to run out, which would
deteriorate the quality of the print master.

[0194] Curing can be partial or full. A partial cure is defined as a
degree of curing wherein at least 5%, preferably 10%, of the functional
groups in the coated formulation is converted. A full cure is defined as
a degree of curing wherein the increase in the percentage of converted
functional groups, with increased exposure to radiation (time and/or
dose), is negligible. A full cure corresponds with a conversion
percentage that is within 10%, preferably 5%, from the maximum conversion
percentage defined by the horizontal asymptote in the RT-FTIR graph
(percentage conversion versus curing energy or curing time).

[0195] The most important parameters when selecting a curing source are
the spectrum and the intensity of the UV-light. Both parameters affect
the speed of the curing.

[0196] Short wavelength UV light (such from a UV-C source) has poor
penetration and enables to cure droplets primarily on the outside.

[0197] A typical UV-C light source is low pressure mercury vapor
electrical discharge bulb. Such a source has a wide spectral distribution
of energy, but with a strong peak in the short wavelength region of the
UV spectrum.

[0198] Long wavelength UV light (such as from a UV-A source) has better
penetration properties. A typical UV-A source is a medium or high
pressure mercury vapor electrical discharge bulb. Recently UV-LEDS have
become commercially available which also emit in the UV-A spectrum and
that have the potential to replace gas discharge bulb UV sources.

[0199] By doping the mercury gas in discharge bulb with iron or gallium,
an emission can be obtained that covers both the UV-A and the UV-C
spectrum.

[0200] The effect of the spectrum and intensity of a curing source on
curing an ink can also be affected by including dyes in an ink that
absorb energy in a part of the spectrum of a curing source.

[0201] The intensity of a curing source has a direct effect on curing
speed. A high intensity results in higher curing speeds. The curing speed
should be sufficiently high to avoid oxygen inhibition of free radicals
that propagate during curing. Such inhibition not only decreases curing
speed, but also negatively affects the conversion ratio of monomer into
polymer.

[0202] An intermediate layer 210, 211 and 212 is preferably immediately
after having being printed a least partially cured so that the layer is
solidified but still contains residual monomer. This approach improves
the adhesion properties of layers that are subsequently printed on top of
each other.

[0203] Partial intermediate curing is possible with UV-C light, UV-A light
or with broad spectrum UV light. The use of UV-C light polymerizes the
outer skin of an intermediate layer. On the other hand, it reduces the
availability of monomer in the outer skin and this negatively impacts the
adhesion between subsequent intermediate layers. A better solution
therefore exists to provide partial curing with a UV-A source under a
nitrogen atmosphere. This solution both suppresses oxygen inhibition and
optimizes adhesion between subsequent intermediate layers.

[0204] A final post curing is realized with UV-C light or with broad
spectrum UV light. Final curing with UV-C light has the property that the
outside skin of the print master is fully hardened.

[0205] It is important to avoid that light--even stray light--from a
curing source reaches the nozzles of a print head, because this would
cause the ink to polymerize in the nozzles, causing them to become
ineffective. For this reason, a curing source and a print head should be
sufficiently space apart, or a screen should be placed in between both.
In the set up of FIG. 10, a solution consists of placing the UV curing
source for example 180 degrees apart from the print head with regard to
the axle of the cylindrical drum.

Building of a Layered Structure, Shingling, Interlacing

[0206] When the apparatus shown in FIG. 9 is used, the print master can be
created by sequentially printing the intermediate layers.

[0207] Printing of the intermediate bitmaps is done layer by layer from
the bottom to the top layer.

[0208] Because of manufacturing tolerances, the droplet volume, speed and
direction may slightly vary between inkjet nozzles. It is well known in
two-dimensional printing that in absence of any compensating measures
this may lead to correlated image quality artifacts such as banding and
streaking.

[0209] Banding and streaking artifacts in the intermediate layers are
effectively suppressed by means of interlacing and shingling techniques
as for example disclosed in the U.S. Pat. No. 6,679,583 assigned to
Agfa-Graphics NV. According to the teachings of this patent, pixels on a
single row or columns of the image are printed by different nozzles. As a
result, the effect of nozzle variation is spatially diffused so that it
becomes less noticeable. This effectively suppresses the visibility of
banding and streaking.

[0210] The droplets that are ejected by a print head have a main velocity
component in the Z direction relative to the substrate. However, since
the print head during printing also moves in the X direction, the
droplets also have a velocity component in that direction. This means
that the landing position in the X direction is affected by the distance
between the print head and the printable substrate. Because printing an
additional layer changes this distance, this effect needs to be
compensate for in order to achieve registration between subsequent
intermediate layers. A first solution consists of digitally shifting an
intermediate bitmap to compensate for the effect. A second solution
consists of moving the print head in the Z direction so that the distance
between the head and the printable surface remains constant. The distance
can be for example be kept constant at 1 mm. For this purpose the profile
meter 940 (FIG. 9) or 1040 (FIG. 10) can be used.